Journal of High Energy Physics, Gravitation and Cosmology, 2019, 5, 140-148
http://www.scirp.org/journal/jhepgc
ISSN Online: 2380-4335
ISSN Print: 2380-4327
DOI:
10.4236/jhepgc.2019.51006 Dec. 20, 2018 140 Journal of High Energy Physics, G
ravitation and Cosmology
Generation Model of Particle Physics with
Excited Rishon States
Brian Albert Robson
Department of Theoretical Physics, Research School of Physics and Engineering, The Australian National University,
Canberra, Australia
Abstract
It is proposed that the Generation Model (GM) of particle physics, which de-
scribes the elementary particles, the six leptons, the six quarks and the three
weak bosons, of the Standard Model (SM) as composite particles in terms of
three kinds of rishons and their antiparticles may be mimicking a simple
r
model, employing only two kinds of rishons and their antiparticles.
Keywords
Generation Model, Rishon, Excited Rishon State
1. Introduction
The Standard Model (SM) [1] of particle physics assumes that the six leptons:
electron neutrino (
e
ν
), electron (
e
), muon neutrino (
µ
ν
), muon (
µ
), tau
neutrino (
τ
ν
), tau (
τ
) and the six quarks: up (
u
), down (
d
), charmed (
c
),
strange (
s
), top (
t
) and bottom (
b
), which are the building blocks of matter, are
elementary
particles. This assumes that the leptons and quarks have no sub-
structure, although there exists considerable indirect evidence to the contrary [2].
This indicates that the leptons and quarks possess no internal energy content
to provide their mass, contrary to the 1905 conclusion of Einstein [3]: the mass
of a body
m
is a measure of its energy content
E
and is given by
2
mEc=
,
where
c
is the speed of light in a vacuum.
Although in the SM, the mass of a hadron, e.g. a proton, arises essentially
(99%) from the energy content of its constituent quarks and gluons, in
agreement with Einsteins conclusion, the masses of the elementary leptons and
quarks are assumed [4] to arise in a completely different manner, involving the
so-called Higgs mechanism [5] [6]. Thus the SM does not provide a
unified
Robson, B.A.
9) Generation Model of Particle Phys-
.
,
Gravitation and Cos
,
, 140-148.
//doi.org/10.4236/jhepgc.2019.51006
October 22, 2018
December 17, 2018
December 20, 2018
9 by author and
Research Publishing Inc.
work is licensed under the Creative
4.0).
Open Access
B. A. Robson
DOI:
10.4236/jhepgc.2019.51006 141 Journal of High Energy Physics, G
ravitation and Cosmology
origin of mass, contrary to Einsteins conclusion. Furthermore, the SM does not
provide any
physical
explanation, as distinct from the purely
mathematical
Higgs mechanism, for the origin of the masses of the leptons and quarks, as
discussed by Lyre [7].
The Generation Model (GM) [2] [8] of particle physics, which was developed
primarily to describe the three generations of leptons and quarks of the SM, [9]
led to a
composite
model of all the elementary particles of the SM: the six leptons,
the six quarks and the weak bosons,
W
and
Z
, mediating the weak interactions.
The composite nature of these elementary particles of the SM, provided their
constituents are
massless
, allows their masses to arise in agreement with Einsteins
conclusion so that the GM provides a
unified
description of the origin of all
mass and hence has no need for the Higgs mechanism to generate the mass of
any particle.
The substructure of leptons and quarks in the GM is described in terms of
three kinds of spin-
1
2
massless elementary particles called rishons,
T
,
V
and
U
and their antiparticles,
T
,
V
and
U
. The
T
-rishon carries electric charge
1
3
Q=+
, while both the
V
-rishon and
U
-rishon are electrically neutral.
Both the
T
-rishon and the
V
-rishon were initially introduced by Harari [10] in
a schematic composite model of leptons and quarks in 1979. Harari named these
two elementary particles of his schematic composite model rishonsafter the
Hebrew word for first or primary.
Also independently in 1979, Shupe [11] introduced a very similar schematic
composite model of leptons and quarks in which the spin-
1
2
massless
elementary particles were called quips(quark inner parts). Again the first
generation of composite leptons and quarks were described in terms of only two
quips:
a
+
with charge
1
3
Q=+
and
0
a
with charge
0Q=
. The
a
+
and
0
a
quips are equivalent to the
T
and
V
rishons of Harari, respectively. Shupe
assumed that there was no mixing of quip and antiquip fields in forming lepton
and quark composites and that both the quip particles and antiquip antiparticles
existed in an s state. With these assumptions, the number of possible charge
states is eight and these may be associated with the first generation of fermions
and their antiparticles. Hararis model essentially made the same assumptions.
The GM [2] [8] is based upon a unified classification scheme of composite
leptons and quarks that employs only three conserved additive quantum
numbers: electric charge
Q
, particle number
p
and generation quantum number
g
. Table 1 gives these three additive quantum numbers allotted in the GM to the
three kinds of rishons. For each rishon additive quantum number
N
, the
corresponding antirishon has the additive quantum number -
N
.
For each composite lepton or quark, the electric charge is related to the
number of
T
-rishons and the number of
T
-antirishons; the particle number
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ravitation and Cosmology
corresponds to the total number of rishons and the total number of antirishons;
while the generation quantum number is associated with the number of
U
-rishons
and the number of
U
-antirishons.
It should be noted that while the
T
-rishon (
1
3
Q=+
) and the
V
-rishon (
0Q=
)
are distinguishable by their electric charges, the
U
-rishon (
0Q=
), which carries
generation quantum number
1g=−
, is not distinguishable from the
V
-rishon
by any physical characteristic: the generation quantum number is not associated
with any physical property of the
U
-rishon.
It appears plausible that the GM, employing three kinds of rishons and
their antiparticles (all tacitly assumed to be in a 1s ground state) may be
mimicking a simpler model, employing only two kinds of rishons and their
antiparticles.
In the following we shall study the possiblity that each composite particle of
the second generation of leptons and quarks has one V-rishon or one
V
-antirishon in an
excited state
,
i.e.
one V-rishon or one
V
-antirishon is not in
the lowest 1s state.
Thus in the new simpler GM, the
U
-rishon and the
U
-antirishon are
essentially replaced by an excited-state
V
-rishon (
*
V
) and an excited-state
V
-antirishon (
*
V
), respectively. In this way the generation additive quantum
number
g
corresponds to the number of excited-state
*
V
-rishons and the
number of excited-state
*
V
-antirishons so that Table 1 may be replaced by
Table 2. It should be noted that the excited-state
*
V
-rishon has generation
quantum number
1g=−
, corresponding to that of the
U
-rishon in the GM.
We shall now discuss this simpler GM, which we shall also name the two-
rishon GM in the following Sections.
Table 1. GM additive quantum numbers for rishons.
rishon
Q
p
g
T
1
3
+
1
3
+
0
V
0
1
3
+
0
U
0
1
3
+
−1
Table 2. Simpler GM additive quantum numbers for rishons.
rishon
Q
p
g
T
1
3
+
1
3
+
0
V
0
1
3
+
0
*
V
0
1
3
+
−1
B. A. Robson
DOI:
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ravitation and Cosmology
2. The Two-Rishon Generation Model
In the GM [2] [8] it is assumed that each of the three kinds of rishons,
T
,
V
and
U
, carries a color charge, red, green or blue, while each of their antiparticles,
T
,
V
and
U
, carries an anticolor charge, antired, antigreen or antiblue. The GM
also assumes that the interaction responsible for binding rishons and antirishons
together to form colorless leptons and colored quarks is analogous to the strong
color interaction, Quantum Chromo-Dynamics (QCD), that binds quarks and
antiquarks together to form colorless baryons and mesons in the SM. [1] In the
GM the color interaction is mediated by massless hypergluons, corresponding to
a local gauged color
()
3SU
symmetry, that are analogous to the massless
gluons, which mediate the QCD color interaction of the SM.
In the two-rishon GM, the rishon structures of the leptons and quarks
comprising the first generation (see
Table 3) remain unchanged, since the first
generation particles and antiparticles do not contain a
U
-rishon or a
U
-antirishon.
It should be noted that contrary to the 1979 Harari-Shupe model, [10] [11] the
GM replaces the
V
-rishon by its antiparticle
V
-antirishon and vice-versa, in
order that the
u
-quark has particle number
1
3
p=+
, corresponding to its
baryon number
1
3
A=+
in the SM.
In the simpler GM the
U
-rishon and the
U
-antirishon of the GM are
replaced by an excited-state
V
-rishon (
*
V
) and an excited-state
V
-antirishon
(
*
V
), respectively. Thus the color structures of the second generation of leptons
and quarks involving
*
V
-rishons or
*
V
-antirishons remain unchanged from
those of the GM, since the
*
V
-rishon and the
*
V
-antirishon are assumed to
carry the same color charges as the
U
-rishon and the
U
-antirishon, respectively.
In the GM the rishon structures of the second generation of leptons and
Table 3. Two-rishon GM of first generation of leptons and quarks.
particle
structure
Q
p
g
e
+
TTT
+1
+1
0
u
TTV
2
3
+
1
3
+
0
d
TVV
1
3
+
1
3
0
e
ν
VVV
0
−1
0
e
ν
VVV
0
+1
0
d
TVV
1
3
1
3
+
0
u
TTV
2
3
1
3
0
e
TTT
−1
−1
0
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ravitation and Cosmology
quarks are the same as the corresponding leptons and quarks of the first
generation plus the addition of a colorless rishon-antirishon pair,
Π
, where
()()
2 ,UVVU

Π=+

(1)
i.e.
a quantum mechanical mixture of (
UV
) and (
VU
) with
0Qp==
but
1g
, respectively. Thus in the simpler GM, we have
()()
**
2 ,VVVV

Π=+

(2)
so that the pattern for the first generation is repeated for the second generation
as in the GM.
Table 4 gives the rishon structures for the second generation of
leptons and quarks in the two-rishon GM, where
Π
is now given by Equation
(2).
It should be noted that for any given transition the generation quantum
number is required to be
conserved
, although each particle of the second
generation has two possible values of
g
. For example, the decay
,W
µ
µν
−−
→+
(3)
at the rishon level may be written [2]
,TTTVVVTTTVVV
Π→Π+
(4)
which proceeds via the two transitions:
(
)
(
)
**
TTTVVVVVVVTTTVVV
→+
(5)
and
()()
**
,TTTVVVVVVVTTTVVV→+
(6)
which take place with equal probabilities. In each case, the additional colorless
rishon-antirishon pair, (
*
VV
) or (
*
VV
), essentially acts as a
spectator
during the
weak interaction process thereby conserving the generation quantum number
g
,
Table 4. Two-rishon GM of second generation of leptons and quarks.
particle
structure
Q
p
g
µ
+
TTTΠ
+1
+1
1±
c
TTVΠ
2
3
+
1
3
+
1±
s
TVVΠ
1
3
+
1
3
1±
µ
ν
VVVΠ
0
−1
1±
µ
ν
VVVΠ
0
+1
1±
s
TVVΠ
1
3
1
3
+
1±
c
TTVΠ
2
3
1
3
1±
µ
TTTΠ
−1
−1
1±
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DOI:
10.4236/jhepgc.2019.51006 145 Journal of High Energy Physics, G
ravitation and Cosmology
which has the value +1 and −1, respectively.
In the GM the rishon structures of the third generation of leptons and quarks
are the same as the corresponding leptons and quarks of the first generation plus
the addition of two rishon-antirishon pairs,
Π
, that are given by Equation (1).
Thus in the simpler GM, the rishon-antirishon pairs,
Π
, are described by
Equation (2). In this way the pattern of the first and second generation is also
continued for the third generation.
Table 5 shows the rishon structures for the
third generation of leptons and quarks in the two-rishon GM.
In the GM the rishon structure of the
τ
+
particle is for example:
()
()()
()()
()
()()
2TTTTTTUVUVUVVUVUUVVUVU

ΠΠ=+++

(7)
and each particle of the third generation is a similar quantum mechanical mixture
of
0,2g
components. In each case, the additional colorless rishon-anti-
rishon pairs, (
UV
) and/or (
VU
), essentially act as
spectators
during any weak
interaction process. Again it should be noted that for any given transition the
generation quantum number is required to be conserved, although each particle
of the third generation now has three possible values of
g
.
Thus in the simpler GM for example, the decay
W
τ
τν
−−
→+
(8)
at the rishon level may be written
,TTTVVVTTTVVVΠΠ→ΠΠ+
(9)
which proceeds via the four transitions:
()()
()
()
****
,TTTVVVVVVVVVVVTTTVVV
→+
(10)
()
()
()
()
****
,TTTVVVVVVVVVVVTTT VVV→+
(11)
()
(
)
()
()
****
,
TTTVVVVVVVVVVVTT TVVV→+
(12)
Table 5. Two-rishon GM of third generation of leptons and quarks
particle
structure
Q
p
g
τ
+
TTTΠΠ
+1
+1
0,2±
t
TTVΠΠ
2
3
+
1
3
+
0,2±
b
TVVΠΠ
1
3
+
1
3
0,2±
τ
ν
VVVΠΠ
0
−1
0,2±
τ
ν
VVVΠΠ
0
+1
0,2±
b
TVVΠΠ
1
3
1
3
+
0,2±
t
TTVΠΠ
2
3
1
3
0,2±
τ
TTTΠΠ
−1
−1
0,2±
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ravitation and Cosmology
()()()()
****
,TTTVVVVVVVVVVVTTTVVV→+
(13)
which take place with equal probabilities. In each case, the additional two
colorless rishon-antirishon pairs,
()()
**
VVVV
,
()()
**
VVVV
,
()()
**
VVVV
or
()()
**
VVVV
act as
spectators
during the weak interaction process, thereby
conserving the generation quantum number
g
, which has the value +2, 0, 0 and
−2, respectively.
To summarize: the replacement of the
U
-rishon and its antiparticle
U
-antirishon of the GM by an excited-state
V
-rishon (
*
V
) and an excited-state
V
-antirishon (
*
V
), respectively, in the simpler GM, leads to an equivalent
model of the three generations of composite leptons and quarks.
3. Excited Rishon States
Since to date there is no direct evidence for any substructure of leptons or
quarks, it is expected that the rishons and/or antirishons of each lepton or quark
are localized within a very small volume of space by the strong QCD color
interactions, acting between the colored rishons and/or antirishons.
In QCD theory, the short-distance behavior of the color interactions in the GM is
dominated by one-hypergluon exchange and is described by a Coulomb-like
potential, analogous to that in atomic systems [12]. Thus it is expected that the
lowest energy or ground rishon state is a 1s state. This was assumed in the
current GM for each of the
T
,
V
and
U
rishons and their antiparticles,
T
,
V
and
U
antirishons.
Indeed the essential reason for introducing the
U
-rishon and its antiparticle
U
-antirishon into the GM was to avoid annihilation processes, if the second
and third generations of leptons and quarks involved colorless rishon-antirishon
pairs
VV
. In the simpler GM, with the rishon-antirishon pair
Π
given by
Equation (2), such annihilation processes are avoided, since the excited-state
V
-rishon (
*
V
) and its antiparticle (
*
V
) will be in an orthogonal quantum state,
i.e.
a 2s state.
For the second and third generations of leptons and quarks, it is expected by
analogy with atomic physics that the
*
V
-rishon and its antiparticle (
*
V
) will
occupy a 2s state [13] [14].
4. Conclusions and Discussion
It has been demonstrated that the GM of particle physics, which describes the
elementary particles of the SM of particle physics as composite particles in terms
of
three
kinds of rishons and their antiparticles, may be replaced by a simpler
equivalent model employing only
two
kinds of rishons and their antiparticles. In
this simpler model that we have called the Two-Rishon Generation Model, the
U
-rishon of the GM has been replaced by an excited-state
*
V
-rishon in a 2s
state.
If the
*
V
-rishon occupies a 2s state in the composite systems describing the
leptons and quarks of both the second and third generations, all the interactions
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involving the leptons and quarks within the framework of the simpler GM are
identical to those of the GM. In addition the simpler GM retains a unified origin
of mass, the same kind of mass hierarchy of leptons and quarks and the same
origin of gravity as the GM [2]. In particular, since the
*
V
-rishon has the same
parity as the
U
-rishon in the GM, the simpler GM also describes the origin of
apparentCP violation in the
00
-KK
system [2] [15].
The two-rishon GM contains fewer elementary particles (21 counting both
particles and antiparticles and their three different color forms plus the mediating
particles of the electromagnetic and the strong interactions) compared with the
GM involving three kinds of rishons (27 elementary particles), which was a
considerable improvement on the SM (61 elementary particles) [2]. In addition,
the two-rishon GM provides a satisfactory understanding of the second and
third generations of composite leptons and quarks that was not achieved in the
1981 dynamical model of Harari and Seiberg [16].
Conflicts of Interest
The author declares no conflicts of interest regarding the publication of this pa-
per.
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